In a small bowl, combine the warm milk, 1 tablespoon of the brown sugar, and the yeast. Let it sit for 5–10 minutes until foamy.
In a large bowl, mix the oats, melted butter, remaining brown sugar, salt, egg, and the yeast mixture. Stir until well combined.
Add the flour, 1 cup at a time, stirring until a soft dough forms. Turn out onto a floured surface and knead for 6–8 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a clean towel, and let rise in a warm place for 1–1.5 hours, until doubled in size.
Punch down the dough, shape into a loaf, and place in a greased 9x5-inch loaf pan. Cover and let rise for another 30–45 minutes, until it crests above the pan.
Preheat the oven to 375°F (190°C). Bake for 30–35 minutes, until golden brown and hollow-sounding when tapped. If the top browns too quickly, tent with foil.
Remove from the pan and cool on a wire rack. Brush with melted butter if desired. Slice and serve.